Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Calculator

✖Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.ⓘ Reduced Pressure [P_r]			+10% -10%
✖Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.ⓘ Critical Pressure [P_c]			+10% -10%
✖Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter a [a_PR]			+10% -10%
✖α-function is a function of temperature and the acentric factor.ⓘ α-function [α]			+10% -10%
✖Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.ⓘ Reduced Molar Volume [V_m,r]			+10% -10%
✖Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.ⓘ Critical Molar Volume [V_m,c]			+10% -10%
✖Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.ⓘ Peng–Robinson Parameter b [b_PR]			+10% -10%

✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters [T]

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Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R])
T = ((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R])
This formula uses 1 Constants, 8 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Reduced Pressure - Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless.
Critical Pressure - (Measured in Pascal) - Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature.
Peng–Robinson Parameter a - Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.
α-function - α-function is a function of temperature and the acentric factor.
Reduced Molar Volume - Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole.
Critical Molar Volume - (Measured in Cubic Meter per Mole) - Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole.
Peng–Robinson Parameter b - Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

STEP 1: Convert Input(s) to Base Unit

Reduced Pressure: 3.675E-05 --> No Conversion Required
Critical Pressure: 218 Pascal --> 218 Pascal No Conversion Required
Peng–Robinson Parameter a: 0.1 --> No Conversion Required
α-function: 2 --> No Conversion Required
Reduced Molar Volume: 11.2 --> No Conversion Required
Critical Molar Volume: 11.5 Cubic Meter per Mole --> 11.5 Cubic Meter per Mole No Conversion Required
Peng–Robinson Parameter b: 0.12 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = ((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R]) --> ((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R])

Evaluating ... ...

T = 0.124177392063826

STEP 3: Convert Result to Output's Unit

0.124177392063826 Kelvin --> No Conversion Required

FINAL ANSWER

0.124177392063826 ≈ 0.124177 Kelvin <-- Temperature

(Calculation completed in 00.020 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Real Gas » Peng Robinson Model of Real Gas » Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

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< Peng Robinson Model of Real Gas Calculators

Pressure of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

LaTeX Go Pressure = (([R]*(Reduced Temperature*Critical Temperature))/((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))

Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters

LaTeX Go Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R])

Temperature of Real Gas using Peng Robinson Equation

LaTeX Go Temperature given CE = (Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R])

Pressure of Real Gas using Peng Robinson Equation

LaTeX Go Pressure = (([R]*Temperature)/(Molar Volume-Peng–Robinson Parameter b))-((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))

Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters Formula

LaTeX Go

What are Real Gases?

Real gases are non ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behavior of real gases, the following must be taken into account:
- compressibility effects;
- variable specific heat capacity;
- van der Waals forces;
- non-equilibrium thermodynamic effects;
- issues with molecular dissociation and elementary reactions with variable composition.

How to Calculate Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters calculator uses Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]) to calculate the Temperature, The Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the degree or intensity of heat present in the volume of real gas. Temperature is denoted by T symbol.

How to calculate Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters using this online calculator? To use this online calculator for Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters, enter Reduced Pressure (P_r), Critical Pressure (P_c), Peng–Robinson Parameter a (a_PR), α-function (α), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c) & Peng–Robinson Parameter b (b_PR) and hit the calculate button. Here is how the Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters calculation can be explained with given input values -> 0.1241 = ((3.675E-05*218)+(((0.1*2)/(((11.2*11.5)^2)+(2*0.12*(11.2*11.5))-(0.12^2)))))*(((11.2*11.5)-0.12)/[R]).

FAQ

What is Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

The Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the degree or intensity of heat present in the volume of real gas and is represented as T = ((P_r*P_c)+(((a_PR*α)/(((V_m,r*V_m,c)^2)+(2*b_PR*(V_m,r*V_m,c))-(b_PR^2)))))*(((V_m,r*V_m,c)-b_PR)/[R]) or Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]). Reduced Pressure is the ratio of the actual pressure of the fluid to its critical pressure. It is dimensionless, Critical Pressure is the minimum pressure required to liquify a substance at the critical temperature, Peng–Robinson parameter a is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas, α-function is a function of temperature and the acentric factor, Reduced Molar Volume of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature per mole, Critical Molar Volume is the volume occupied by gas at critical temperature and pressure per mole & Peng–Robinson parameter b is an empirical parameter characteristic to equation obtained from Peng–Robinson model of real gas.

How to calculate Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters?

The Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters formula is defined as the degree or intensity of heat present in the volume of real gas is calculated using Temperature = ((Reduced Pressure*Critical Pressure)+(((Peng–Robinson Parameter a*α-function)/(((Reduced Molar Volume*Critical Molar Volume)^2)+(2*Peng–Robinson Parameter b*(Reduced Molar Volume*Critical Molar Volume))-(Peng–Robinson Parameter b^2)))))*(((Reduced Molar Volume*Critical Molar Volume)-Peng–Robinson Parameter b)/[R]). To calculate Temperature of Real Gas using Peng Robinson Equation given Reduced and Critical Parameters, you need Reduced Pressure (P_r), Critical Pressure (P_c), Peng–Robinson Parameter a (a_PR), α-function (α), Reduced Molar Volume (V_m,r), Critical Molar Volume (V_m,c) & Peng–Robinson Parameter b (b_PR). With our tool, you need to enter the respective value for Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume & Peng–Robinson Parameter b and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Temperature?

In this formula, Temperature uses Reduced Pressure, Critical Pressure, Peng–Robinson Parameter a, α-function, Reduced Molar Volume, Critical Molar Volume & Peng–Robinson Parameter b. We can use 3 other way(s) to calculate the same, which is/are as follows -

Temperature = Reduced Temperature*(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Temperature = Reduced Temperature*(sqrt((Peng–Robinson Parameter a*(Pressure/Reduced Pressure))/(0.45724*([R]^2))))
Temperature = Reduced Temperature*((Peng–Robinson Parameter b*(Pressure/Reduced Pressure))/(0.07780*[R]))

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